Mathematics- Solution to Exercise on the previous tutorial

I posted a tutorial on COMBINATION some days ago
, so at the end of the tutorial I dropped some exercises which will be solved now, in case you missed the tutorial click here Mathematics tutorial on Combination

The questions go thus;

b. How many committees of five can be formed from 8 men and 4 women if each committee is to have at least 2 women?

Solution

a) We are to simplify here and that can be done using the combination formula.

Is it clear? now let's do the second question.

b. By reading the question, we are to select 5 committees from 8 men and 4 women. But it was stated that each committee must have at least 2 women

i) We can have 3 men and 2 women.

ii) We can have 1 man and 4 women.

Can you tell me the next arrangement?

Think!

iii) We can have 3 women and 2 men.

Do you also get that?

Okay, let's simplify i, ii and iii

So the numbers of ways to select five committees with at least two women are,
( 1568 + 560 +1568)ways which are 3696ways.

Pictures: All pictures used in this post was created by me using math editor app.

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